Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 9 (2013), 015, 13 pages      arXiv:1301.1432      http://dx.doi.org/10.3842/SIGMA.2013.015

On a Trivial Family of Noncommutative Integrable Systems

Andrey V. Tsiganov
St. Petersburg State University, St. Petersburg, Russia

Received October 17, 2012, in final form February 18, 2013; Published online February 22, 2013

Abstract
We discuss trivial deformations of the canonical Poisson brackets associated with the Toda lattices, relativistic Toda lattices, Henon-Heiles, rational Calogero-Moser and Ruijsenaars-Schneider systems and apply one of these deformations to construct a new trivial family of noncommutative integrable systems.

Key words: bi-Hamiltonian geometry; noncommutative integrable systems.

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